APC 2004 MC

Physics C: Mechanics

PHYSICS C

Section I, MECHANICSTime-45 minutes

35 Questions

Directions: Each of the questions or incomplete statements below is'followed by five suggested answers orcompletions. Select the one that is best in each case and then fill in the corresponding oval on the answer sheet.

Note: To simplify calculations, you may use g = 10 m/ s2 in all problems.

1. The graph above shows velocity u versus time rfor an object in linear motion. Which of the follow-ing is a possible graph of position x versus time rfor this object?

2. An object is dropped from rest from the top of a400 m cliff on Earth. If air resistance is negligible,what is the distance the object travels during thefirst 6 s of its fall?

(A) 30 m(B) 60 m(C) 120 m(D) 180 m(E) 360 m

(A) (B)

(C) x (D) xl-'. Lo!\ '" oFa*,l\_ |

(E) x

x

F,,ht,

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t,

Questions 5-6

Force (N)

Time t (s)

A block of mass 3 kg, initially at rest, is pulledalong a frictionless, horizontal surface with a forceshown as a function of time r by the graph above.

5. The acceleration of the block at / = 2 s is

(A) 3l4mlsz(B) 413 m/s2(C) 2m/s2(D) 8 m/s2

(E) lTmlsz

6. The speed of the block at t = 2 s is

(A) 4/3 m/s(B) 8/3 m/s(C) 4mls(D) 8 m/s(E) 24mls

of..l.,1o Floor

3. A2 kg ball collides with the floor at an angle 0and rebounds at the same angle and speed as

shown above. Which of the following vectorsrepresents the impulse exerted on the ball by thefloor?

(A) |I

Ii

7(c)

(D)

(B)\

(E)

I

ffiF4. Three blocks of masses 3m, 2m, and m are

connectedto snings A, B, ar;rd C as shownabove. The blocks are pulled along a roughsurface by a force of magnitude F exerted bysfting C. The coeffrcient of friction between each

' block and the surface is the same. Which stringmust be the strongest in order not to break?

. (A)Ar: (B) B

(C) C,. (D) They must all be the same strength.

;1 (E) It is impossible to determine without knowing:i the coefficient of friction.

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Questions 7-8

A sphere of mass M, radius r, and rotationalinertia / is released from rest at the top of an inclinedplane of height lr as shown above.

7. If the plane is frictionless, what is the speed u",n

of the center of mass of the sphere at the bottomof the incline?

(q ^ITEE

,o, 2Mgh\"/ __T_

,n, ZMghr2\.-/ __l_


An object weighing 300 N is suspended by meansof two cords, as shown above. The tension in thehorizontal cord is

(A) 0N(B) ls0 N(c) 210 N(D) 300 N(E) 400 N

9.

(D)

(E)

8. Ifthe plane has friction so that the sphere rollswithout slipping, what is the speed ur^ of thecenter of mass at the bottom of the incline?

(N JTEE

@ry,", 2Mghr2\-,, I/n\ w\"/ 1l-7-

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Questions 10-12

A small box is on a ramp tilted at an angle 0 :.

above the horizontal. The box may be subject to the

following forces: frictional (/), gravitational (mg),

pulling or pushing. (& )*A normal (M). In the

following free-body diagrams for the box, the lengths

of the vectors are proportional to the magnitudes ofthe forces.

Figure A

Figure B

Figure C

Figure D

mg cos 0

Figure E

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10. Which figure best represents the free-bodydiagram for the box if it is accelerating up theramp?

(A) Figure A(B) Figure B(C) Figure C(D) Figure D(E) Figure E

11. Which figure best represents the free-bodydiagram for the box if it is at rest on the ramp?

' (A) Figure A(B) Figure B(C) Figure C(D) Figure D(E) Figure E

12. Which figure best represents the free-bodydiagram for the box if it is sliding down theramp at constant speed?

(A) Figure A(B) Figure B(C) Figure C(D) Figure D(E) Figure E

13. The momentum p of amoving object as a functionof time I is given by the expression p = Ict3, whereft is a constant. The force causing this motion isgiven by the expression

(A) 3H2

ah2(B) ?

::i

lil

.)

t:

;l:'l

i,,

i:'

:l

ii'i

:I

s+(D) H4

@)+

127

.:i:.

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----a--'

P

14. A spacecraft orbits Earth in a circular orbit ofradius R, as shown above. When the spacecraftis at position P shown, a short burst of the ship'sengines resulg in a small increase in its speed.The new orbit is best shown by the solid curvein which of the following diagrams?

,-----a

(A)

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15. A student holds one end of a string in a fixedposition. A ball of mass 0.2 kg attached to theother end of the string moves in a horizontalcircle of radius 0.5 m with a constant speed of5 m/s. How much work is done on the ball bvthe string during each revolution?

(A) 0J(B) 0.s J(c) 1.0J(D) 2nJ(E) 5a J

16. A wheel of 0.5 m radius rolls without slippingon a horizontal surface. The axle of the wheeladvances at constant velocity, moving a distanceof20 m in 5 s. The angular speed ofthe wheelabout its point of contact on the surface is

(A) 2radians.s-l(B) 4radians.s-r(C) 8radians.s-r(D) 16 radians . s-r(E) 3zradians . s-l

t-_lI lBoardtltltltlSkater | |o---*-l--l

Top View

17. A long board is free to slide on a sheet offrictionless ice. As shown in the top viewabove, a skater skates to the board and hopsonto one end, causing the board t6 sfide androtate. In this situation, which of the followingoccurs?

(A) Linear momentum is converted to angularmomentum.

(B) Kinetic energy is converted to angularmomentum.

Rotational kinetic energy is conserved.Translational kinetic energy is conserved.Linear momentum and angular momentum

are both conserved.

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II

(c)(D)(E)

@III

'P.'-.-<" ,

f-t\y

1.28


Questions 18-19

A simple pendulum has a period of 2 s for small''amplitude oscillations.

18. The length of the pendulum is most nearly

(A) 1/6 m(B) 1/4 m(C) r/2m(D) lm(E) 2m

19. Which of the following equations could representthe angle 0 that the pendulum makes with thevertical as a function of time t ?

(A) d = 9''* sA[t(B) d = 9n,* sin nt

(C) d = 9n'* sin 2nt

(D) I = 9rno sin 4nt

@) e = 0^u sin Szt

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Two blocks of masses M and m, with M > m, areconnected by a light string. The string passes overa frictionless pulley of negligible mass so that theblocks hang vertically. The blocks are then releasedfrom rest. What is the acceleration of the block ofmass M ?

(A) g

M-m\b)Mg

M+m\e)MgM+m\u) u -mEM-m\n) u+mE

For a particular nonlinear spring, the relationshipbetween the magnitude of the applied force F andthe resultant displacement x from equilibriumis given by the equation F = lc*. What is theamount of work done by stretching the spring adistance -ro ?

(A) rrJ

?0.

2r.

(B) i*'**:

t*:t*;

(c)

(D)

(E)

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Questions 22-23

Physics C: Mechanics,

25. As shown above, two students sit at opposite endsof a boat that is initially at rest. The student in thefront throws a heavy ball to the student in the back.What is the motion of the boat at the time immedi-ately after the ball is thrown and, later, after theball is caught? (Assume that air and water frictionare negligible.)

ImmediatelyAfter the Throw After the Catch

(A) Boat moves forward Boat moves forward(B) Boat moves forward Boat moves backward(C) Boat moves forward Boat does not move(D) Boat moves backward Boat does not move@) Boat moves backward Boat moves forward

nr2.0 m/s\_/*

1.5 kgf

1.0 n/s

Q +.0 tg

Two pucks moving on a frictionless air table areabout to collide, as shown above. The 1.5 kg puck ismoving directly east at 2.0 m/s. The 4.0 kg puck ismoving directly north at 1.0 m/s.

22. What is the total kinetic energy of the two-pucksystem before the collision?

(A) Jtr I(B) s.0 J(c) 7.0 J(D) 10 J(E) 11 J

23. What is the magnitude of the total momentum ofthe two-puck system after the collision?

(A) 1.0kg'm/s(B) 3.5 kg.m/s(C) 5.0 kg.m/s(D) 7.0 kg.m/s(E) 5.sJ5 kg.m/s

24. T\e position of an object is given by the equationx=3.0t2 + I.5t + 4.5,where x is inmetersand / is in seconds. What is the instantaneousacceleration of the object at t = 3.0 s?

(A) 3.0 m/s2

(B) 6.0 m/s2

(C) 9.0 m/s2

(D) 19.5 m/s2

(E) 36 m/s2

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Two blocks are joined by a light string that passes

over the pulley shown above, which has radius R

and moment of inertia 1 about its center. 4 and

T2 are the tensions in the string on either side ofthe pulley and a is the angular acceleration ofthe pulley. Which of the following equations best

describes the pulley's rotational motion during the

time the blocks accelerate?

(A) mrgR = Ia(B) (4 + T2)R = Ia(C) T2R = Ia(D) (4 - rt)R = Ia(E) (*" - mr)gR = Ia

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-R"Rz

The graph above shows the force of gravity on a

small mass as a function of its distance R fromthe center of the Earth of radius R", if the Eanh isassumed to have a uniform density. The workdone by the force of gravity when the small mass

approaches Earth from far away and is placed intoa circular orbit of radius R2 is best represented bythe area under the curve between

(A) R=0andR=R"(B) R=.0andR=Rz(C) R-R"and R=Rz(D) R=R,andR=-(E) R=RzandR=-

27.

Force

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28. A horizontal force F pushes a block of mass nlagainst a vertical wall. The coefficient of frictionbetween the block and the wall is p. What value

of F is necessary to keep the block from slippingdown the wall?

(A) me

(B) pms

rct m8\-/ u

(D) ms(r - p)

(E) ms(l + p)

29. A mass M suspended by a spring with force

constant k has a period I when set into oscillation

on Earth. Its period on Mars, whose mass is aboutt1E

*d radius ) that of Earth, is most nearly


30. A 1000 W electric motor lifts a 100 kg safe at

constant velocity. The vertical distance throughwhich the motor can raise the safe in 10 s ismost nearly

(A) 1m(B) 3m(C) 10 m(D) 32m(E) 100 m

31 . A I .0 kg mass is attached to the end of a verticalideal spring with a force constant of 400 N/m.The mass is set in simple harmonic motion with an

amplitude of 10 cm. The speed of the 1.0 kg mass

at the equilibrium position is

(A) 2n{s(B) 4mls(C) 20 m/s(D) 40 m/s(E) 200 m/s

32. A student is testing the kinematic equations foruniformly accelerated motion by measuring the

time it takes for lighrweight plastic balls to fallto the floor from a height of 3 m in the lab. Thestudent predicts the time to fall using g as

9.80 mf s2 but finds the measured time to be

35Vo greater. Which of the following is the mostlikely cause of the large percent error?

(A) The acceleration due to gravity is707o

greater than 9.80 mf s2 atthis location.

(B) The acceleration due to gravity is 707o less

than 9.80 ^f "' utthis location.

(C) Air resistance increases the downwardacceleration.

(D) The acceleration of the plastic balls is notuniform.

(E) The plastic balls are not truly spherical.

(A)

(B)

(c)

)rJ

7+rJ

T

ro> t,(E) 3r

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Note: Figure not drawn to scale.

An object is thrown with velocity v from theedge of a cliff above level ground. Neglect airresistance. In order for the object to travel amaximum horizontal distance from the cliffbefore hitting the ground, the throw should beat an angle 0 with respect to the horizontal of

(A) greater than'60' above the horizontal(B) greater than 45o but less than 60' above

the horizontal(C) greater than zero but less than 45o above

the horizontal(D) zero(E) greater than zero but less than 45o below

the horizontal

34. A car travels forward with constant velocity. Itgoes over a small stone, which gets stuck in thegroove of a tire. The initial acceleration of thestone, as it leaves the surface of the road, is

(A) vertically upward(B) horizontally forward(C) horizontally backward(D) zero(E) upward and forward, at approximately 45o

to the horizontal

35. The escape speed for a rocket at Earth's surfaceis r.r, . What would be the rocket's escape speed

from the surface of a planet with twice Earth'smass and the same radius as Earth?

(A) 2u"(B) JTu"(c) u"

ue

J'ue

2

(D)

(E)

END OF SECTION I, MECHANICS

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APC 2004 MC

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